Conformal invariance in two dimensions is a very powerful tool which gives rise to many non-pertubative relations constraining dynamics of 2d CFTs. Among them is universality of stress-energy tensor sector [1]}, namely any correlation function which includes only stress-energy tensor and its descendants depends only on central charge \(c\)  but not on any other details of the theory. An analytic form of all such correlators can in principle be found in a recursive form [2]}.
The stress-energy sector can be regarded as integrable, even if the whole theory is understood to be chaotic [3]}.
This can be justified formally by noting there is an infinite number of mutually commuting quantum KdV charges [4]}, [5]}, [6]} – local charges \(Q_{2n-1}\)  of the form
\(Q_{2n-1}={1\over 2\pi }\int _0^{2\pi } T_{2n}(\varphi )\, d\varphi ,\) 
